We recover unknown source terms in nonlinear hyperbolic differential equations and in nonlinear parabolic integro-differential equations in one space variable under the assumption of knowing a first integral (in the hyperbolic case) or the value of the solution at a point inside the domain (in the parabolic case). For this class of problems we prove existence results in classes of smooth solutions. Moreover, for linear hyperbolic and parabolic differential equations in one space variable we recover some characteristic parameters.
We consider the asymptotic analysis for the linear Boltzmann equation with elastic and inelastic scattering. The physical model describes the motion of test particles propagating by elastic and inelastic collisions through a host medium in the Lorentz gas limit. The background is in thermodynamical equilibrium with only two internal energy levels. We apply the compressed Chapman-Enskog procedure to derive the diffusive-type approximations in the cases of dominant elastic and dominant inelastic collisions. Then we present numerical examples showing the time evolution of the distribution function in some physically relevant cases. In the appendix the successive overrelaxation method is briefly cutlined.
The European Space Agency will launch in January 2003 a mission called “Rosetta” to visit a comet. This space-craft will rendezvous with comet Wirtanen, follow it on its way to the sun in a close orbit and observe the comet core from this position. As part of the mission, a small package is carried, the “Rosetta Lander”, which separates and lands softly on the surface of the comet, where it will carry out a sequence of scientific investigations.
The purpose of the talk is to review some of the recent results on Gorenstein liaison confronting them with classical results in complete intersection liaison theory.
Numerical methods for the evaluation of 2D integrals, based on bivariate quasi-interpolating splines, with a four directional mesh, are presented and convergence results are derived. Moreover an application to 2D singular integrals, defined in the Hadamard finite part sense, is proposed and studied.
The classical problem of small denominators is revisited in its historical development, ending with recent results on exponential stability.
Lo scopo di questo testo è di presentare i temi principali riguardanti le correnti positive su varietà complesse. L’importanza di questo strumento, per coloro che studiano geometria complessa, è evidente; tuttavia non è semplice tenere le fila di una grande quantità di contributi sull’argomento, alcuni dei quali sono ormai pietre miliari su questa via. Vorremmo quindi delineare una “mappa” dei contributi che ci sono sembrati particolarmente significativi; per ovvie ragioni, rimandiamo ai test originali non appena si voglia entrare nel merito dei singoli argomenti.
